###Defining the distance matrix###
def Dist(G):
n=G.order()
M=zero_matrix(QQ,n,n)
for i in range(n):
for j in range(i+1,n):
x=G.distance(i,j)
M[i,j]=x
M[j,i]=x
return M
|
|
# Definition of transmission sequence
def trs(G):
n=G.order()
ones = ones_matrix(n,1)
dg=G.distance_matrix()
trg=vector(dg*ones)
trgs=trg.list()
trgs.sort()
return trgs
# Checks if a graph is transmission regular
def IsTrsReg(G):
unique_list_t=[]
trans=list(trs(G))
for y in trans:
if y not in unique_list_t:
unique_list_t.append(y)
if len(unique_list_t)==1:
return True
else:
return False
|
|
#### COSPECTRALITY #####
|
|
### Distance cospectral mates on 7 vertices
L7=[]
for G in graphs.cospectral_graphs(7, matrix_function=Dist, graphs=lambda g: g.is_connected()):
L7.append([i.graph6_string() for i in G])
L7
[['FnlkG', 'F~LKg'],
['F|UL?', 'FlVKG'],
['FzLNW', 'F~L[g'],
['FnLKg', 'FlkNG'],
['FlKlG', 'FpJ^?'],
['FhmL?', 'FxeK_'],
['Fl[KW', 'FlMkG'],
['F|^[g', 'F|\\lg'],
['Fx}L?', 'F|mK_'],
['FllkG', 'F|LLG'],
['F|NkG', 'Fl{MW']]
[['FnlkG', 'F~LKg'],
['F|UL?', 'FlVKG'],
['FzLNW', 'F~L[g'],
['FnLKg', 'FlkNG'],
['FlKlG', 'FpJ^?'],
['FhmL?', 'FxeK_'],
['Fl[KW', 'FlMkG'],
['F|^[g', 'F|\\lg'],
['Fx}L?', 'F|mK_'],
['FllkG', 'F|LLG'],
['F|NkG', 'Fl{MW']]
|
### Distance cospectral mates on 8 vertices
L8=[]
for G in graphs.cospectral_graphs(8, matrix_function=Dist, graphs=lambda g: g.is_connected()):
L8.append([i.graph6_string() for i in G])
L8
WARNING: Output truncated!full_output.txt
[['Gj\\nvg', 'GbT~~g'],
['Gv\\\\[s', 'GzX\\}c'],
['Gvx|Ro', 'GztmRk'],
['Gl]N@?', 'GtUn@?'],
['GvI[P?', 'GfA|P?'],
['Gj@m\\G', 'GvO[{C'],
['GbwkV?', 'GfakTO'],
['GzclTG', 'GvoX{C'],
['Gjml@C', 'GjslPC'],
['GzSlVG', 'Gr]kV_'],
['GjolTG', 'GrPlpG'],
['GjlkT?', 'GzOlpG'],
['Gr_kP?', 'GdEMD?'],
['GrzX[c', 'GzZX[c'],
['Gne{TG', 'GvsY[S'],
['GzQkTO', 'G|Ul@O'],
['GbD~|O', 'GfonvO'],
['GrxW{c', 'GvW[[k'],
['Gn`lR_', 'GjekRo'],
['Gr]{V?', 'GrwW\\s'],
['GfF|tW', 'Gr|X[s'],
['GnEkTG', 'GrO[{S'],
['GbWmv?', 'Glc}DO'],
['Gv_LtW', 'GvC}Do'],
['Gvx[{c', 'Gr|[[s'],
['GzY]xG', 'GzY^PK'],
['Gjikv?', 'GzP[XK'],
['GvEkRo', 'GrfKTK'],
['GjolR?', 'GjIlR?'],
['Gva{^?', 'Gb{{VO', 'GjxlR_'],
['G~Y]xG', 'Gzy^PK'],
['Gv@}z_', 'GzZmpG'],
['Gr|][c', 'Gv|X[c'],
['GvYKH?', 'Gr]M@?'],
['Gz{lVW', 'Gv{]{c'],
['GbL||W', 'GvSmvS'],
['GbTntG', 'GrSk\\['],
['GnolvO', 'Grz[[c'],
['GnC}DO', 'GvQY[C'],
['GnMKP?', 'GtUN@?'],
['GrOz^C', 'GvXW{c'],
['GbTntg', 'Grsk^K'],
['Grq[[S', 'GrqW[['],
['Gv@}Z_', 'GzYmpG'],
['GrRY|C', 'GvoY[['],
['G~LlTO', 'Gvw[{S'],
['Gr_nP?', 'Gvck@C'],
['Gv|X[s', 'Gvz\\[c'],
['GvQ^\\C', 'GzRZ\\C'],
['GfiKT?', 'GtYL@O'],
['GvCLTk', 'Grq][C'],
['GrLltO', 'GvSkvO'],
['G~DlT?', 'GvcLPk'],
['Gfmkvg', 'GbSn~K'],
['GbGlv?', 'GvCKP['],
['GbTntk', 'GrX^]c'],
['GztkT?', 'Gvd{T?'],
['GbTn|k', 'GzX^]c'],
['GnFKP?', 'GvQ[P?'],
...
['Gfi{V?', 'GnkkTG'],
['GbtlTG', 'GrwW\\c'],
['Gn]kTG', 'G~SlTG'],
['GjX}TG', 'GvTW{S'],
['Gj`lR_', 'GvOW[['],
['GrSkTW', 'GvoX[C'],
['GvoW{C', 'GrO\\{C'],
['GjTlT?', 'GbOkvS'],
['Gb{{VG', 'GbS{Vk', 'Gj[kVK'],
['GjSltW', 'GrX[{c'],
['GvGkTG', 'GvSG{C'],
['G|UKH?', 'Gd]kH?'],
['GdqL@?', 'G`pNH?'],
['GzokTG', 'GvQ[[C'],
['GbtmR?', 'GjYkR_'],
['Gz[m^K', 'Gvz[\\c'],
['GvYLH?', 'GvXkH?'],
['Gvq{VO', 'Gr}kV_'],
['GjWkv?', 'GzcmR?'],
['Gf]|TG', 'GvZ[[c'],
['GfK{VO', 'GrO\\|C'],
['GjxlR?', 'GzInR?'],
['GzWmv?', 'GrPnxG'],
['GzQkR?', 'G|Ql@O'],
['Gb{{VW', 'GbS{V{', 'GzmkRo'],
['G~e{VG', 'GbT{V{', 'Gj||R_'],
['GjOntG', 'Gjk{TG'],
['Grk{VG', 'GbSk^['],
['G~OlT?', 'GrcKT['],
['Gba{V?', 'GjokTG'],
['GfNkP?', 'GvFLP?'],
['GvQktG', 'GfMkV_'],
['GzDltO', 'GrU{VO'],
['GrZ\\pG', 'GrW^[c'],
['GjT}DO', 'GrT[{C'],
['GfWlTO', 'GbWlv?'],
['GzOlTG', 'Gro[{C'],
['Gf?nz_', 'GnwkR_'],
['GbF\\x?', 'GfS{x?'],
['GjIlvG', 'GvoX|C'],
['Gb[kTW', 'GrcW{S'],
['G~{k|k', 'G~X]^s'],
['GvwlT?', 'GzklPC'],
['GbTnvK', 'GrSk^{'],
['GbwkvO', 'GvpW{C'],
['Grsk\\K', 'GjSl\\K'],
['GrGmv?', 'GrPmpG'],
['GzolTG', 'GvQ\\[C'],
['GzDlTO', 'GrqW{c'],
['GnakDC', 'GhmND?'],
['GbckvO', 'GbEkVo'],
['Gre{TG', 'Grs[{C'],
['GbR}\\G', 'Gb}kRo'],
['G~EkRo', 'Gr\\W{c'],
['GzPmR_', 'GvSW{c'],
['GzTnTG', 'GvyW[k'],
['GfZ}|G', 'GzSn^K'],
['Gf@kz_', 'Grc}DO'],
['GjQmtG', 'GbS{VK'],
['GzGkv?', 'GrS[{C']]
WARNING: Output truncated!full_output.txt
[['Gj\\nvg', 'GbT~~g'],
['Gv\\\\[s', 'GzX\\}c'],
['Gvx|Ro', 'GztmRk'],
['Gl]N@?', 'GtUn@?'],
['GvI[P?', 'GfA|P?'],
['Gj@m\\G', 'GvO[{C'],
['GbwkV?', 'GfakTO'],
['GzclTG', 'GvoX{C'],
['Gjml@C', 'GjslPC'],
['GzSlVG', 'Gr]kV_'],
['GjolTG', 'GrPlpG'],
['GjlkT?', 'GzOlpG'],
['Gr_kP?', 'GdEMD?'],
['GrzX[c', 'GzZX[c'],
['Gne{TG', 'GvsY[S'],
['GzQkTO', 'G|Ul@O'],
['GbD~|O', 'GfonvO'],
['GrxW{c', 'GvW[[k'],
['Gn`lR_', 'GjekRo'],
['Gr]{V?', 'GrwW\\s'],
['GfF|tW', 'Gr|X[s'],
['GnEkTG', 'GrO[{S'],
['GbWmv?', 'Glc}DO'],
['Gv_LtW', 'GvC}Do'],
['Gvx[{c', 'Gr|[[s'],
['GzY]xG', 'GzY^PK'],
['Gjikv?', 'GzP[XK'],
['GvEkRo', 'GrfKTK'],
['GjolR?', 'GjIlR?'],
['Gva{^?', 'Gb{{VO', 'GjxlR_'],
['G~Y]xG', 'Gzy^PK'],
['Gv@}z_', 'GzZmpG'],
['Gr|][c', 'Gv|X[c'],
['GvYKH?', 'Gr]M@?'],
['Gz{lVW', 'Gv{]{c'],
['GbL||W', 'GvSmvS'],
['GbTntG', 'GrSk\\['],
['GnolvO', 'Grz[[c'],
['GnC}DO', 'GvQY[C'],
['GnMKP?', 'GtUN@?'],
['GrOz^C', 'GvXW{c'],
['GbTntg', 'Grsk^K'],
['Grq[[S', 'GrqW[['],
['Gv@}Z_', 'GzYmpG'],
['GrRY|C', 'GvoY[['],
['G~LlTO', 'Gvw[{S'],
['Gr_nP?', 'Gvck@C'],
['Gv|X[s', 'Gvz\\[c'],
['GvQ^\\C', 'GzRZ\\C'],
['GfiKT?', 'GtYL@O'],
['GvCLTk', 'Grq][C'],
['GrLltO', 'GvSkvO'],
['G~DlT?', 'GvcLPk'],
['Gfmkvg', 'GbSn~K'],
['GbGlv?', 'GvCKP['],
['GbTntk', 'GrX^]c'],
['GztkT?', 'Gvd{T?'],
['GbTn|k', 'GzX^]c'],
['GnFKP?', 'GvQ[P?'],
...
['Gfi{V?', 'GnkkTG'],
['GbtlTG', 'GrwW\\c'],
['Gn]kTG', 'G~SlTG'],
['GjX}TG', 'GvTW{S'],
['Gj`lR_', 'GvOW[['],
['GrSkTW', 'GvoX[C'],
['GvoW{C', 'GrO\\{C'],
['GjTlT?', 'GbOkvS'],
['Gb{{VG', 'GbS{Vk', 'Gj[kVK'],
['GjSltW', 'GrX[{c'],
['GvGkTG', 'GvSG{C'],
['G|UKH?', 'Gd]kH?'],
['GdqL@?', 'G`pNH?'],
['GzokTG', 'GvQ[[C'],
['GbtmR?', 'GjYkR_'],
['Gz[m^K', 'Gvz[\\c'],
['GvYLH?', 'GvXkH?'],
['Gvq{VO', 'Gr}kV_'],
['GjWkv?', 'GzcmR?'],
['Gf]|TG', 'GvZ[[c'],
['GfK{VO', 'GrO\\|C'],
['GjxlR?', 'GzInR?'],
['GzWmv?', 'GrPnxG'],
['GzQkR?', 'G|Ql@O'],
['Gb{{VW', 'GbS{V{', 'GzmkRo'],
['G~e{VG', 'GbT{V{', 'Gj||R_'],
['GjOntG', 'Gjk{TG'],
['Grk{VG', 'GbSk^['],
['G~OlT?', 'GrcKT['],
['Gba{V?', 'GjokTG'],
['GfNkP?', 'GvFLP?'],
['GvQktG', 'GfMkV_'],
['GzDltO', 'GrU{VO'],
['GrZ\\pG', 'GrW^[c'],
['GjT}DO', 'GrT[{C'],
['GfWlTO', 'GbWlv?'],
['GzOlTG', 'Gro[{C'],
['Gf?nz_', 'GnwkR_'],
['GbF\\x?', 'GfS{x?'],
['GjIlvG', 'GvoX|C'],
['Gb[kTW', 'GrcW{S'],
['G~{k|k', 'G~X]^s'],
['GvwlT?', 'GzklPC'],
['GbTnvK', 'GrSk^{'],
['GbwkvO', 'GvpW{C'],
['Grsk\\K', 'GjSl\\K'],
['GrGmv?', 'GrPmpG'],
['GzolTG', 'GvQ\\[C'],
['GzDlTO', 'GrqW{c'],
['GnakDC', 'GhmND?'],
['GbckvO', 'GbEkVo'],
['Gre{TG', 'Grs[{C'],
['GbR}\\G', 'Gb}kRo'],
['G~EkRo', 'Gr\\W{c'],
['GzPmR_', 'GvSW{c'],
['GzTnTG', 'GvyW[k'],
['GfZ}|G', 'GzSn^K'],
['Gf@kz_', 'Grc}DO'],
['GjQmtG', 'GbS{VK'],
['GzGkv?', 'GrS[{C']]
|
### Distance cospectral mates on 9 vertices
L9=[]
for G in graphs.cospectral_graphs(9, matrix_function=Dist, graphs=lambda g: g.is_connected()):
L9.append([i.graph6_string() for i in G])
L9
WARNING: Output truncated!full_output.txt
[['HlS}IeR', 'HlKmhFJ'],
['HlSimVb', 'HnCinEj'],
['HlThyFB', 'HlkmLEJ'],
['Hhn~LU?', 'HlyNxm?'],
['H~MyKMH', 'Hjoi}eR'],
['HntigN_', 'HvLWtn?'],
['HjCm[Em', 'Hjc]KFi'],
['Hzt\\[u?', 'Hjunku?'],
['Hjc[kMo', 'Hh]KLUW'],
['HlTwNMb', 'H|diHFj'],
['HhdkHEj', 'HhdiHEj'],
['H|t{^EB', 'H|TJxUx', 'Hnxk{fS'],
['HnFjKfN', 'HnFmHfZ'],
['HjCLK]g', 'HlcJHMc'],
['HjewK]l', 'Hltk{EY'],
['H|{kyVR', 'Hlf}^eH'],
['HjUgkmO', 'HlKNKUg'],
['H|knwEH', 'HhtIZVJ'],
['HlkMkEg', 'H|Sh{EO'],
['Hnk[]EO', 'H|Ik]ES'],
['HjkmKMi', 'Hhej]Ew'],
['H~SkjUZ', 'HlTi}Uf'],
['Hzcn[Ek', 'HldigF^'],
['Hhe}{Ew', 'HhugNNX'],
['HhSgKFV', 'HlShLU@'],
['H|ShJUz', 'HlTgmFv'],
['HjVGNmW', 'HjfwMMg'],
['H|fiH]L', 'H|fINUL'],
['Hl{gjeB', 'HlshjeB'],
['HhcjKEz', 'HxdWLmB'],
['HzmHkEG', 'H|FGLMH'],
['Hhki{EW', 'H|DwHEL', 'HhdI\\UB'],
['HjkILFW', 'HldXKEw'],
['HjCM[Ni', 'HrKYeEy'],
['HlSwkmS', 'HlI^MEa'],
['HlunheJ', 'HnEyjEn'],
['H|SngF\\', 'HlCijfn'],
['Hle|KF_', 'HzE[KmP'],
['HlkjzEH', 'HhlnJEJ'],
['Hntw~EB', 'Hlxw{fs'],
['HhK|{EW', 'HhKW}}O'],
['H|UhIUv', 'HlvwZeB'],
['Hjcl[U_', 'H~DKGmP'],
['HnN]OEQ', 'Hxhjkm?'],
['HjKWeM?', 'HxHHgm?'],
['Hnc}jFh', 'HnIL~M['],
['Hxyl{f[', 'Hnhw^nS'],
['Hjkn\\Ea', 'H|fLkUI'],
['HxIyKFa', 'Hdim{E_'],
['HhtIXVJ', 'HhWh\\E}'],
['HxWl[eO', 'HjGz\\E_'],
['Hh{G[}?', 'HjINwM?'],
['H~SnyUR', 'HnD}JnX'],
['H~clKMi', 'Hlsl}EB', 'HnDyJE\\', 'Hh|kZEJ', 'HxWl\\eX'],
['HlDWKn_', 'H|Eg[UO'],
['HnSgiFF', 'H|NKHUH'],
['H|{gYUr', 'H~kjHEZ'],
['H|Un\\EJ', 'H|snLUJ'],
['HlSjIFN', 'HlSmYFb'],
...
['H~dX[u?', 'Hhymlm?'],
['HnVi}Er', 'H|fmh]h'],
['HhM{KM_', 'H`gNhfA'],
['H|dh[EG', 'Hh{g\\EW'],
['H~uHKUg', 'HlI^NEa'],
['H~Um]M}', 'Hnnj\\uL'],
['Hh{j[eX', 'Hh{jKuX'],
['H|ShnEb', 'Hdg]Vfi'],
['HhcNlEY', 'HnDGinc'],
['HjCg^]i', 'Hn]gmEQ'],
['HjtILfB', 'HlIk^Es'],
['HjeMgM?', 'HniWgM?'],
['H|SnYuR', 'H~dLL^H', 'HnF\\L]X', 'Hldnxeh', 'HlD}LnX', 'H|dmLmJ'],
['HzE[KeO', 'Hl[KSUK'],
['HjS|[fO', 'Hhi[~Eo'],
['HnC}NMH', 'HlD}JNH'],
['HnDzlMH', 'HjfMHVN'],
['H~}m^uR', 'H|nz\\}J'],
['Hx]nmEQ', 'HjDyMmx'],
['HhdLXEb', 'HhdJXEb'],
['HnDJwFH', 'HnDIJfH'],
['H~CWLMh', 'HjEWLNp', 'Hj[l[EQ', 'HnShGFZ', 'HnOk{fO'],
['HxCmNE]', 'HhCnnE['],
['HjKg~U?', 'HjSymU?'],
['H|cjGEZ', 'HjtGZeB'],
['H||IXEJ', 'Hh{W}uo'],
['HxSL[UW', 'HlcJ[Ug'],
['HnkI}m?', 'HnxNgm?'],
['H|lmXUz', 'H|\\MxUz', 'Hn|mxUh'],
['HnShjEV', 'H|Li\\MH'],
['HnviHe~', 'HnuyJe^', 'Hl}~LE\\'],
['Hjcl[E_', 'H|og{EO'],
['H|{n^EJ', 'H~knXEz'],
['H|SknUR', 'HnKiLf\\'],
['HnUGL}\\', 'H||{hf?'],
['H~UwI}R', 'H|\\JHUz'],
['H|lM|uZ', 'H|zn[f['],
['H|uj~Er', 'HlVzjfZ'],
['HlSiZEj', 'HlSjheJ'],
['Hjg]}eO', 'HjwY}eO'],
['H|~kKEU', 'HxK~{Ew'],
['H~TYNuX', 'H~{jXFJ'],
['Hj{jKEX', 'H|swNEB', 'HndyHMH', 'HnWw[fS'],
['Hhk{[U_', 'HxGh^ES'],
['H~{nH]L', 'Hz||Hef'],
['H|fmlEL', 'H|cmn]H'],
['HlVg}Vr', 'H|dmh^h'],
['Hx{hMUQ', 'HlKi\\]H'],
['H|SL{EW', 'H|U{[EO'],
['HnK[KEi', 'HltHgN_'],
['H|mN|Eg', 'H|f{LmD'],
['HxYg[uO', 'HnGYMEq'],
['Hx{gkU?', 'H~IXoM?'],
['HhKjWU?', 'HhKGb}?'],
['HllIJfH', 'Hl|IHmH'],
['HhJloFo', 'HhJgwFq'],
['HnC~jFj', 'H~om|eR'],
['H||ikEu', 'H|SlJVr'],
['HxkH{UW', 'Hxe|KEg', 'Hzg~KE_'],
['HxeJW]?', 'HngWkm?']]
WARNING: Output truncated!full_output.txt
[['HlS}IeR', 'HlKmhFJ'],
['HlSimVb', 'HnCinEj'],
['HlThyFB', 'HlkmLEJ'],
['Hhn~LU?', 'HlyNxm?'],
['H~MyKMH', 'Hjoi}eR'],
['HntigN_', 'HvLWtn?'],
['HjCm[Em', 'Hjc]KFi'],
['Hzt\\[u?', 'Hjunku?'],
['Hjc[kMo', 'Hh]KLUW'],
['HlTwNMb', 'H|diHFj'],
['HhdkHEj', 'HhdiHEj'],
['H|t{^EB', 'H|TJxUx', 'Hnxk{fS'],
['HnFjKfN', 'HnFmHfZ'],
['HjCLK]g', 'HlcJHMc'],
['HjewK]l', 'Hltk{EY'],
['H|{kyVR', 'Hlf}^eH'],
['HjUgkmO', 'HlKNKUg'],
['H|knwEH', 'HhtIZVJ'],
['HlkMkEg', 'H|Sh{EO'],
['Hnk[]EO', 'H|Ik]ES'],
['HjkmKMi', 'Hhej]Ew'],
['H~SkjUZ', 'HlTi}Uf'],
['Hzcn[Ek', 'HldigF^'],
['Hhe}{Ew', 'HhugNNX'],
['HhSgKFV', 'HlShLU@'],
['H|ShJUz', 'HlTgmFv'],
['HjVGNmW', 'HjfwMMg'],
['H|fiH]L', 'H|fINUL'],
['Hl{gjeB', 'HlshjeB'],
['HhcjKEz', 'HxdWLmB'],
['HzmHkEG', 'H|FGLMH'],
['Hhki{EW', 'H|DwHEL', 'HhdI\\UB'],
['HjkILFW', 'HldXKEw'],
['HjCM[Ni', 'HrKYeEy'],
['HlSwkmS', 'HlI^MEa'],
['HlunheJ', 'HnEyjEn'],
['H|SngF\\', 'HlCijfn'],
['Hle|KF_', 'HzE[KmP'],
['HlkjzEH', 'HhlnJEJ'],
['Hntw~EB', 'Hlxw{fs'],
['HhK|{EW', 'HhKW}}O'],
['H|UhIUv', 'HlvwZeB'],
['Hjcl[U_', 'H~DKGmP'],
['HnN]OEQ', 'Hxhjkm?'],
['HjKWeM?', 'HxHHgm?'],
['Hnc}jFh', 'HnIL~M['],
['Hxyl{f[', 'Hnhw^nS'],
['Hjkn\\Ea', 'H|fLkUI'],
['HxIyKFa', 'Hdim{E_'],
['HhtIXVJ', 'HhWh\\E}'],
['HxWl[eO', 'HjGz\\E_'],
['Hh{G[}?', 'HjINwM?'],
['H~SnyUR', 'HnD}JnX'],
['H~clKMi', 'Hlsl}EB', 'HnDyJE\\', 'Hh|kZEJ', 'HxWl\\eX'],
['HlDWKn_', 'H|Eg[UO'],
['HnSgiFF', 'H|NKHUH'],
['H|{gYUr', 'H~kjHEZ'],
['H|Un\\EJ', 'H|snLUJ'],
['HlSjIFN', 'HlSmYFb'],
...
['H~dX[u?', 'Hhymlm?'],
['HnVi}Er', 'H|fmh]h'],
['HhM{KM_', 'H`gNhfA'],
['H|dh[EG', 'Hh{g\\EW'],
['H~uHKUg', 'HlI^NEa'],
['H~Um]M}', 'Hnnj\\uL'],
['Hh{j[eX', 'Hh{jKuX'],
['H|ShnEb', 'Hdg]Vfi'],
['HhcNlEY', 'HnDGinc'],
['HjCg^]i', 'Hn]gmEQ'],
['HjtILfB', 'HlIk^Es'],
['HjeMgM?', 'HniWgM?'],
['H|SnYuR', 'H~dLL^H', 'HnF\\L]X', 'Hldnxeh', 'HlD}LnX', 'H|dmLmJ'],
['HzE[KeO', 'Hl[KSUK'],
['HjS|[fO', 'Hhi[~Eo'],
['HnC}NMH', 'HlD}JNH'],
['HnDzlMH', 'HjfMHVN'],
['H~}m^uR', 'H|nz\\}J'],
['Hx]nmEQ', 'HjDyMmx'],
['HhdLXEb', 'HhdJXEb'],
['HnDJwFH', 'HnDIJfH'],
['H~CWLMh', 'HjEWLNp', 'Hj[l[EQ', 'HnShGFZ', 'HnOk{fO'],
['HxCmNE]', 'HhCnnE['],
['HjKg~U?', 'HjSymU?'],
['H|cjGEZ', 'HjtGZeB'],
['H||IXEJ', 'Hh{W}uo'],
['HxSL[UW', 'HlcJ[Ug'],
['HnkI}m?', 'HnxNgm?'],
['H|lmXUz', 'H|\\MxUz', 'Hn|mxUh'],
['HnShjEV', 'H|Li\\MH'],
['HnviHe~', 'HnuyJe^', 'Hl}~LE\\'],
['Hjcl[E_', 'H|og{EO'],
['H|{n^EJ', 'H~knXEz'],
['H|SknUR', 'HnKiLf\\'],
['HnUGL}\\', 'H||{hf?'],
['H~UwI}R', 'H|\\JHUz'],
['H|lM|uZ', 'H|zn[f['],
['H|uj~Er', 'HlVzjfZ'],
['HlSiZEj', 'HlSjheJ'],
['Hjg]}eO', 'HjwY}eO'],
['H|~kKEU', 'HxK~{Ew'],
['H~TYNuX', 'H~{jXFJ'],
['Hj{jKEX', 'H|swNEB', 'HndyHMH', 'HnWw[fS'],
['Hhk{[U_', 'HxGh^ES'],
['H~{nH]L', 'Hz||Hef'],
['H|fmlEL', 'H|cmn]H'],
['HlVg}Vr', 'H|dmh^h'],
['Hx{hMUQ', 'HlKi\\]H'],
['H|SL{EW', 'H|U{[EO'],
['HnK[KEi', 'HltHgN_'],
['H|mN|Eg', 'H|f{LmD'],
['HxYg[uO', 'HnGYMEq'],
['Hx{gkU?', 'H~IXoM?'],
['HhKjWU?', 'HhKGb}?'],
['HllIJfH', 'Hl|IHmH'],
['HhJloFo', 'HhJgwFq'],
['HnC~jFj', 'H~om|eR'],
['H||ikEu', 'H|SlJVr'],
['HxkH{UW', 'Hxe|KEg', 'Hzg~KE_'],
['HxeJW]?', 'HngWkm?']]
|
### To find cospectral graphs on 10 vertices, first sort the graphs in to groups of potentially cospectral graphs
Num1 = 545
Num2 = 5279
Num_Vertices = 10
L = []
for i in range(Num2):
L.append([i,[]])
for G in graphs(Num_Vertices):
if G.is_connected():
a=Dist(G).charpoly()(Num1)
b=mod(a, Num2)
L[b][1].append(G.graph6_string())
|
|
### Checking within each group for sets with similar characteristic polynomial evaluated at a prime
N=[]
for i in range(Num2):
K=[]
M=[]
for j in range(len(L[i][1])):
a=Dist(Graph(L[i][1][j])).charpoly()(167)
K.append([L[i][1][j],a])
for i in range(len(K)):
A=[K[i][0]]
for j in range(i+1,len(K)):
if K[i][1]-K[j][1]==0:
A.append(K[j][0])
if len(A)>1:
N.append(A)
|
|
### Checking each of these sets for cospectrality. This is our set of cospectral graphs on 10 vertices
L10=[]
for i in range(len(N)):
K=[]
M=[]
for j in range(len(N[i])):
a=Dist(Graph(N[i][j])).charpoly()
K.append([N[i][j],a])
for i in range(len(K)):
A=[K[i][0]]
for j in range(i+1,len(K)):
if K[i][1]-K[j][1]==0:
A.append(K[j][0])
if len(A)>1:
L10.append(A)
|
|
##### GIRTH #######
|
|
### Finds cospectral graphs with different girth, no results on 7
for x in L7:
unique_list = []
girths=[]
for y in x:
girths.append(Graph(y).girth())
for y in girths:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
print x
print unique_list
|
|
### Finds cospectral graphs with different girth, no results on 8
for x in L8:
unique_list = []
girths=[]
for y in x:
girths.append(Graph(y).girth())
for y in girths:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
print x
print unique_list
|
|
### Finds cospectral graphs with different girth
for x in L9:
unique_list = []
girths=[]
for y in x:
girths.append(Graph(y).girth())
for y in girths:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
print x
print unique_list
['HlDHKUG', 'HlDHGEJ'] [4, 3] ['HlDHKUG', 'HlDHGEJ'] [4, 3] |
A1=Graph('HlDHKUG')
A2=Graph('HlDHGEJ')
|
|
A1
|
A2
|
A1.girth()
4 4 |
A2.girth()
3 3 |
### Checks the graphs are cospectral
Dist(A1).charpoly()-Dist(A2).charpoly()
0 0 |
Dist(A1).charpoly()
x^9 - 112*x^7 - 758*x^6 - 1994*x^5 - 2010*x^4 + 184*x^3 + 1262*x^2 + 193*x - 222 x^9 - 112*x^7 - 758*x^6 - 1994*x^5 - 2010*x^4 + 184*x^3 + 1262*x^2 + 193*x - 222 |
#### PLANARITY, DEGREE SEQUENCE, TRANSMISSION SEQUENCE, AND NUMBER OF CONNECTED COMPONENTS OF THE COMPLEMENT
|
|
### Finds cospectral graphs with where one is planar and one is not
for x in L7:
unique_list = []
planar=[]
for y in x:
planar.append(Graph(y).is_planar())
for y in planar:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
print x
print unique_list
['FnlkG', 'F~LKg'] [True, False] ['FzLNW', 'F~L[g'] [True, False] ['F|^[g', 'F|\\lg'] [True, False] ['FllkG', 'F|LLG'] [True, False] ['FnlkG', 'F~LKg'] [True, False] ['FzLNW', 'F~L[g'] [True, False] ['F|^[g', 'F|\\lg'] [True, False] ['FllkG', 'F|LLG'] [True, False] |
### Finds cospectral graphs with different transmission sequences
for x in L7:
unique_list=[]
transseq=[]
for y in x:
transseq.append(trs(Graph(y)))
for y in transseq:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
print x
print unique_list
['FnlkG', 'F~LKg']
[[8, 8, 8, 8, 8, 8, 10], [7, 8, 8, 8, 9, 9, 9]]
['F|UL?', 'FlVKG']
[[7, 8, 9, 9, 10, 10, 11], [8, 8, 8, 9, 9, 11, 11]]
['FzLNW', 'F~L[g']
[[7, 7, 7, 8, 9, 9, 9], [6, 8, 8, 8, 8, 9, 9]]
['FnLKg', 'FlkNG']
[[7, 8, 9, 9, 9, 9, 9], [8, 8, 8, 8, 9, 9, 10]]
['FlKlG', 'FpJ^?']
[[7, 9, 9, 9, 9, 9, 10], [8, 8, 8, 9, 9, 10, 10]]
['FhmL?', 'FxeK_']
[[8, 8, 8, 10, 10, 10, 10], [7, 9, 9, 9, 10, 10, 10]]
['Fl[KW', 'FlMkG']
[[7, 9, 9, 9, 9, 9, 10], [8, 8, 8, 9, 9, 10, 10]]
['F|^[g', 'F|\\lg']
[[7, 7, 7, 8, 8, 8, 9], [6, 8, 8, 8, 8, 8, 8]]
['Fx}L?', 'F|mK_']
[[7, 7, 7, 9, 10, 10, 10], [6, 8, 8, 8, 10, 10, 10]]
['FllkG', 'F|LLG']
[[8, 8, 8, 8, 9, 9, 10], [7, 8, 9, 9, 9, 9, 9]]
['F|NkG', 'Fl{MW']
[[7, 7, 7, 9, 9, 9, 10], [6, 8, 8, 8, 9, 9, 10]]
['FnlkG', 'F~LKg']
[[8, 8, 8, 8, 8, 8, 10], [7, 8, 8, 8, 9, 9, 9]]
['F|UL?', 'FlVKG']
[[7, 8, 9, 9, 10, 10, 11], [8, 8, 8, 9, 9, 11, 11]]
['FzLNW', 'F~L[g']
[[7, 7, 7, 8, 9, 9, 9], [6, 8, 8, 8, 8, 9, 9]]
['FnLKg', 'FlkNG']
[[7, 8, 9, 9, 9, 9, 9], [8, 8, 8, 8, 9, 9, 10]]
['FlKlG', 'FpJ^?']
[[7, 9, 9, 9, 9, 9, 10], [8, 8, 8, 9, 9, 10, 10]]
['FhmL?', 'FxeK_']
[[8, 8, 8, 10, 10, 10, 10], [7, 9, 9, 9, 10, 10, 10]]
['Fl[KW', 'FlMkG']
[[7, 9, 9, 9, 9, 9, 10], [8, 8, 8, 9, 9, 10, 10]]
['F|^[g', 'F|\\lg']
[[7, 7, 7, 8, 8, 8, 9], [6, 8, 8, 8, 8, 8, 8]]
['Fx}L?', 'F|mK_']
[[7, 7, 7, 9, 10, 10, 10], [6, 8, 8, 8, 10, 10, 10]]
['FllkG', 'F|LLG']
[[8, 8, 8, 8, 9, 9, 10], [7, 8, 9, 9, 9, 9, 9]]
['F|NkG', 'Fl{MW']
[[7, 7, 7, 9, 9, 9, 10], [6, 8, 8, 8, 9, 9, 10]]
|
### Finds cospectral graphs with different degree sequences
for x in L7:
unique_list=[]
degseq=[]
for y in x:
degseq.append(Graph(y).degree_sequence())
for y in degseq:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
print x
print unique_list
['FnlkG', 'F~LKg']
[[4, 4, 4, 4, 4, 4, 2], [5, 4, 4, 4, 3, 3, 3]]
['F|UL?', 'FlVKG']
[[5, 4, 3, 3, 3, 2, 2], [4, 4, 4, 3, 3, 2, 2]]
['FzLNW', 'F~L[g']
[[5, 5, 5, 4, 3, 3, 3], [6, 4, 4, 4, 4, 3, 3]]
['FnLKg', 'FlkNG']
[[5, 4, 3, 3, 3, 3, 3], [4, 4, 4, 4, 3, 3, 2]]
['FlKlG', 'FpJ^?']
[[5, 3, 3, 3, 3, 3, 2], [4, 4, 4, 3, 3, 2, 2]]
['FhmL?', 'FxeK_']
[[4, 4, 4, 2, 2, 2, 2], [5, 3, 3, 3, 2, 2, 2]]
['Fl[KW', 'FlMkG']
[[5, 3, 3, 3, 3, 3, 2], [4, 4, 4, 3, 3, 2, 2]]
['F|^[g', 'F|\\lg']
[[5, 5, 5, 4, 4, 4, 3], [6, 4, 4, 4, 4, 4, 4]]
['Fx}L?', 'F|mK_']
[[5, 5, 5, 3, 2, 2, 2], [6, 4, 4, 4, 2, 2, 2]]
['FllkG', 'F|LLG']
[[4, 4, 4, 4, 3, 3, 2], [5, 4, 3, 3, 3, 3, 3]]
['F|NkG', 'Fl{MW']
[[5, 5, 5, 3, 3, 3, 2], [6, 4, 4, 4, 3, 3, 2]]
['FnlkG', 'F~LKg']
[[4, 4, 4, 4, 4, 4, 2], [5, 4, 4, 4, 3, 3, 3]]
['F|UL?', 'FlVKG']
[[5, 4, 3, 3, 3, 2, 2], [4, 4, 4, 3, 3, 2, 2]]
['FzLNW', 'F~L[g']
[[5, 5, 5, 4, 3, 3, 3], [6, 4, 4, 4, 4, 3, 3]]
['FnLKg', 'FlkNG']
[[5, 4, 3, 3, 3, 3, 3], [4, 4, 4, 4, 3, 3, 2]]
['FlKlG', 'FpJ^?']
[[5, 3, 3, 3, 3, 3, 2], [4, 4, 4, 3, 3, 2, 2]]
['FhmL?', 'FxeK_']
[[4, 4, 4, 2, 2, 2, 2], [5, 3, 3, 3, 2, 2, 2]]
['Fl[KW', 'FlMkG']
[[5, 3, 3, 3, 3, 3, 2], [4, 4, 4, 3, 3, 2, 2]]
['F|^[g', 'F|\\lg']
[[5, 5, 5, 4, 4, 4, 3], [6, 4, 4, 4, 4, 4, 4]]
['Fx}L?', 'F|mK_']
[[5, 5, 5, 3, 2, 2, 2], [6, 4, 4, 4, 2, 2, 2]]
['FllkG', 'F|LLG']
[[4, 4, 4, 4, 3, 3, 2], [5, 4, 3, 3, 3, 3, 3]]
['F|NkG', 'Fl{MW']
[[5, 5, 5, 3, 3, 3, 2], [6, 4, 4, 4, 3, 3, 2]]
|
### Finds cospectral graphs with a different number of complement connected components
for x in L7:
unique_list = []
components=[]
for y in x:
Gbar=Graph(y).complement()
components.append(Gbar.connected_components_number())
for y in components:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
print x
print unique_list
['FzLNW', 'F~L[g']
[1, 2]
['F|^[g', 'F|\\lg']
[1, 2]
['Fx}L?', 'F|mK_']
[1, 2]
['F|NkG', 'Fl{MW']
[1, 2]
['FzLNW', 'F~L[g']
[1, 2]
['F|^[g', 'F|\\lg']
[1, 2]
['Fx}L?', 'F|mK_']
[1, 2]
['F|NkG', 'Fl{MW']
[1, 2]
|
### This pair of graphs has all four properties
B1=Graph('F|^[g')
B2=Graph('F|\\lg')
|
|
B1
|
B2
|
B1.complement()
|
B2.complement()
|
trs(B1)
[7, 7, 7, 8, 8, 8, 9] [7, 7, 7, 8, 8, 8, 9] |
trs(B2)
[6, 8, 8, 8, 8, 8, 8] [6, 8, 8, 8, 8, 8, 8] |
B1.degree_sequence()
[5, 5, 5, 4, 4, 4, 3] [5, 5, 5, 4, 4, 4, 3] |
B2.degree_sequence()
[6, 4, 4, 4, 4, 4, 4] [6, 4, 4, 4, 4, 4, 4] |
B1.is_planar()
True True |
B2.is_planar()
False False |
### Checks the graphs are cospectral
Dist(B1).charpoly()-Dist(B2).charpoly()
|
|
Dist(B1).charpoly()
x^7 - 39*x^5 - 142*x^4 - 180*x^3 - 72*x^2 x^7 - 39*x^5 - 142*x^4 - 180*x^3 - 72*x^2 |
#### TRANSMISSION REGULARITY (evidence of no example on <=10 vertices)
|
|
### Finds cospectral graphs with different transmission sequence, no results on 7
for x in L7:
unique_list=[]
transseq=[]
for y in x:
transseq.append(trs(Graph(y)))
for y in transseq:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
for y in x:
if IsTrsReg(Graph(y))==True:
print x
print unique_list
|
|
### Finds cospectral graphs with different transmission sequence, no results on 8
for x in L8:
unique_list=[]
transseq=[]
for y in x:
transseq.append(trs(Graph(y)))
for y in transseq:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
for y in x:
if IsTrsReg(Graph(y))==True:
print x
print unique_list
|
|
### Finds cospectral graphs with different transmission sequence, no results on 9
for x in L9:
unique_list=[]
transseq=[]
for y in x:
transseq.append(trs(Graph(y)))
for y in transseq:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
for y in x:
if IsTrsReg(Graph(y))==True:
print x
print unique_list
|
|
### Finds cospectral graphs with different transmission sequence, no results on 10
for x in L10:
unique_list=[]
transseq=[]
for y in x:
transseq.append(trs(Graph(y)))
for y in transseq:
if y not in unique_list:
unique_list.append(y)
if len(unique_list)>1:
for y in x:
if IsTrsReg(Graph(y))==True:
print x
print unique_list
|
|
|
|